LMFDB - Embedded newform 560.3.br.b.369.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,3,Mod(129,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.129"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	560.br (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.2588948042$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 42x^{14} + 1322x^{12} + 17616x^{10} + 175407x^{8} + 205392x^{6} + 203018x^{4} + 23226x^{2} + 2401 $ x^16 + 42x^14 + 1322x^12 + 17616x^10 + 175407x^8 + 205392x^6 + 203018x^4 + 23226*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			369.8
Root			$2.51048 - 4.34828i$ of defining polynomial
Character	$\chi$	$=$	560.369
Dual form			560.3.br.b.129.8

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.51048 + 4.34828i) q^{3} +(-4.93710 + 0.790609i) q^{5} +(-2.74755 - 6.43824i) q^{7} +(-8.10505 + 14.0384i) q^{9} +(4.76531 + 8.25377i) q^{11} -15.1849 q^{13} +(-15.8323 - 19.4831i) q^{15} +(-11.6790 - 20.2287i) q^{17} +(9.15855 + 5.28769i) q^{19} +(21.0976 - 28.1102i) q^{21} +(-18.2632 - 10.5443i) q^{23} +(23.7499 - 7.80663i) q^{25} -36.2016 q^{27} -37.0510 q^{29} +(-13.4505 + 7.76565i) q^{31} +(-23.9265 + 41.4419i) q^{33} +(18.6551 + 29.6140i) q^{35} +(-16.9168 - 9.76693i) q^{37} +(-38.1214 - 66.0282i) q^{39} -37.7426i q^{41} +18.2540i q^{43} +(28.9166 - 75.7167i) q^{45} +(-0.155040 + 0.268537i) q^{47} +(-33.9019 + 35.3788i) q^{49} +(58.6400 - 101.567i) q^{51} +(8.87784 - 5.12562i) q^{53} +(-30.0523 - 36.9821i) q^{55} +53.0986i q^{57} +(3.10758 - 1.79416i) q^{59} +(96.8741 + 55.9303i) q^{61} +(112.651 + 13.6111i) q^{63} +(74.9693 - 12.0053i) q^{65} +(-11.0746 + 6.39394i) q^{67} -105.885i q^{69} +32.7865 q^{71} +(-30.1530 - 52.2266i) q^{73} +(93.5691 + 83.6728i) q^{75} +(40.0468 - 53.3579i) q^{77} +(-45.6617 + 79.0884i) q^{79} +(-17.9382 - 31.0698i) q^{81} -103.825 q^{83} +(73.6535 + 90.6374i) q^{85} +(-93.0158 - 161.108i) q^{87} +(-52.3329 - 30.2144i) q^{89} +(41.7213 + 97.7639i) q^{91} +(-67.5345 - 38.9911i) q^{93} +(-49.3972 - 18.8650i) q^{95} -130.271 q^{97} -154.492 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{5} - 12 q^{9} + 12 q^{11} + 28 q^{15} + 12 q^{19} - 8 q^{21} - 42 q^{25} - 136 q^{29} - 84 q^{31} + 190 q^{35} - 312 q^{39} + 384 q^{45} + 296 q^{49} + 76 q^{51} + 372 q^{59} + 348 q^{61} - 104 q^{65}+ \cdots - 176 q^{99}+O(q^{100}) $ 16 * q - 6 * q^5 - 12 * q^9 + 12 * q^11 + 28 * q^15 + 12 * q^19 - 8 * q^21 - 42 * q^25 - 136 * q^29 - 84 * q^31 + 190 * q^35 - 312 * q^39 + 384 * q^45 + 296 * q^49 + 76 * q^51 + 372 * q^59 + 348 * q^61 - 104 * q^65 + 384 * q^71 + 150 * q^75 - 148 * q^79 - 140 * q^81 + 580 * q^85 - 912 * q^89 + 616 * q^91 + 310 * q^95 - 176 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	2.51048	+	4.34828i	0.836828	+	1.44943i	0.892534	+	0.450981i	$0.148926\pi$
$3$	2.51048	+	4.34828i	0.836828	+	1.44943i	−0.0557061	+	0.998447i	$0.517741\pi$
$4$		0			0
$5$	−4.93710	+	0.790609i	−0.987420	+	0.158122i
$5$	−4.93710	+	0.790609i	−0.987420	+	0.158122i
$6$		0			0
$7$	−2.74755	−	6.43824i	−0.392508	−	0.919749i
$7$	−2.74755	−	6.43824i	−0.392508	−	0.919749i
$8$		0			0
$9$	−8.10505	+	14.0384i	−0.900561	+	1.55982i
$10$		0			0
$11$	4.76531	+	8.25377i	0.433210	+	0.750342i	0.997148	−	0.0754753i	$-0.0240474\pi$
$11$	4.76531	+	8.25377i	0.433210	+	0.750342i	−0.563937	+	0.825818i	$0.690714\pi$
$12$		0			0
$13$	−15.1849			−1.16807			−0.584034	−	0.811729i	$-0.698527\pi$
$13$	−15.1849			−1.16807			−0.584034	+	0.811729i	$0.698527\pi$
$14$		0			0
$15$	−15.8323	−	19.4831i	−1.05549	−	1.29887i
$16$		0			0
$17$	−11.6790	−	20.2287i	−0.687002	−	1.18992i	−0.972803	−	0.231633i	$-0.925593\pi$
$17$	−11.6790	−	20.2287i	−0.687002	−	1.18992i	0.285802	−	0.958289i	$-0.407740\pi$
$18$		0			0
$19$	9.15855	+	5.28769i	0.482029	+	0.278300i	0.721262	−	0.692663i	$-0.243563\pi$
$19$	9.15855	+	5.28769i	0.482029	+	0.278300i	−0.239233	+	0.970962i	$0.576896\pi$
$20$		0			0
$21$	21.0976	−	28.1102i	1.00465	−	1.33858i
$22$		0			0
$23$	−18.2632	−	10.5443i	−0.794053	−	0.458447i	0.0473345	−	0.998879i	$-0.484927\pi$
$23$	−18.2632	−	10.5443i	−0.794053	−	0.458447i	−0.841387	+	0.540432i	$0.818261\pi$
$24$		0			0
$25$	23.7499	−	7.80663i	0.949995	−	0.312265i
$26$		0			0
$27$	−36.2016			−1.34080
$28$		0			0
$29$	−37.0510			−1.27762			−0.638810	−	0.769365i	$-0.720573\pi$
$29$	−37.0510			−1.27762			−0.638810	+	0.769365i	$0.720573\pi$
$30$		0			0
$31$	−13.4505	+	7.76565i	−0.433887	+	0.250505i	−0.701001	−	0.713160i	$-0.747263\pi$
$31$	−13.4505	+	7.76565i	−0.433887	+	0.250505i	0.267114	+	0.963665i	$0.413930\pi$
$32$		0			0
$33$	−23.9265	+	41.4419i	−0.725045	+	1.25581i
$34$		0			0
$35$	18.6551	+	29.6140i	0.533002	+	0.846114i
$36$		0			0
$37$	−16.9168	−	9.76693i	−0.457212	−	0.263971i	0.253660	−	0.967294i	$-0.418366\pi$
$37$	−16.9168	−	9.76693i	−0.457212	−	0.263971i	−0.710871	+	0.703322i	$0.751699\pi$
$38$		0			0
$39$	−38.1214	−	66.0282i	−0.977471	−	1.69303i
$40$		0			0
$41$		−	37.7426i		−	0.920552i	−0.887776	−	0.460276i	$-0.847751\pi$
$41$		−	37.7426i		−	0.920552i	0.887776	−	0.460276i	$-0.152249\pi$
$42$		0			0
$43$			18.2540i			0.424512i	0.977214	+	0.212256i	$0.0680810\pi$
$43$			18.2540i			0.424512i	−0.977214	+	0.212256i	$0.931919\pi$
$44$		0			0
$45$	28.9166	−	75.7167i	0.642590	−	1.68259i
$46$		0			0
$47$	−0.155040	+	0.268537i	−0.00329872	+	0.00571355i	−0.867670	−	0.497141i	$-0.834383\pi$
$47$	−0.155040	+	0.268537i	−0.00329872	+	0.00571355i	0.864371	+	0.502854i	$0.167717\pi$
$48$		0			0
$49$	−33.9019	+	35.3788i	−0.691875	+	0.722017i
$50$		0			0
$51$	58.6400	−	101.567i	1.14980	−	1.99152i
$52$		0			0
$53$	8.87784	−	5.12562i	0.167506	−	0.0967099i	−0.413903	−	0.910321i	$-0.635835\pi$
$53$	8.87784	−	5.12562i	0.167506	−	0.0967099i	0.581410	+	0.813611i	$0.302501\pi$
$54$		0			0
$55$	−30.0523	−	36.9821i	−0.546406	−	0.672403i
$56$		0			0
$57$			53.0986i			0.931555i
$58$		0			0
$59$	3.10758	−	1.79416i	0.0526708	−	0.0304095i	−0.473433	−	0.880830i	$-0.656986\pi$
$59$	3.10758	−	1.79416i	0.0526708	−	0.0304095i	0.526104	+	0.850420i	$0.323652\pi$
$60$		0			0
$61$	96.8741	+	55.9303i	1.58810	+	0.916890i	0.993620	+	0.112779i	$0.0359753\pi$
$61$	96.8741	+	55.9303i	1.58810	+	0.916890i	0.594480	+	0.804111i	$0.297358\pi$
$62$		0			0
$63$	112.651	+	13.6111i	1.78812	+	0.216049i
$64$		0			0
$65$	74.9693	−	12.0053i	1.15337	−	0.184697i
$66$		0			0
$67$	−11.0746	+	6.39394i	−0.165293	+	0.0954319i	−0.580364	−	0.814357i	$-0.697090\pi$
$67$	−11.0746	+	6.39394i	−0.165293	+	0.0954319i	0.415072	+	0.909789i	$0.363757\pi$
$68$		0			0
$69$		−	105.885i		−	1.53456i
$70$		0			0
$71$	32.7865			0.461781			0.230891	−	0.972980i	$-0.425836\pi$
$71$	32.7865			0.461781			0.230891	+	0.972980i	$0.425836\pi$
$72$		0			0
$73$	−30.1530	−	52.2266i	−0.413055	−	0.715433i	0.582167	−	0.813069i	$-0.302205\pi$
$73$	−30.1530	−	52.2266i	−0.413055	−	0.715433i	−0.995222	+	0.0976365i	$0.968872\pi$
$74$		0			0
$75$	93.5691	+	83.6728i	1.24759	+	1.11564i
$76$		0			0
$77$	40.0468	−	53.3579i	0.520088	−	0.692960i
$78$		0			0
$79$	−45.6617	+	79.0884i	−0.577997	+	1.00112i	0.417712	+	0.908579i	$0.362832\pi$
$79$	−45.6617	+	79.0884i	−0.577997	+	1.00112i	−0.995709	+	0.0925400i	$0.970501\pi$
$80$		0			0
$81$	−17.9382	−	31.0698i	−0.221459	−	0.383578i
$82$		0			0
$83$	−103.825			−1.25091			−0.625453	−	0.780262i	$-0.715086\pi$
$83$	−103.825			−1.25091			−0.625453	+	0.780262i	$0.715086\pi$
$84$		0			0
$85$	73.6535	+	90.6374i	0.866512	+	1.06632i
$86$		0			0
$87$	−93.0158	−	161.108i	−1.06915	−	1.85182i
$88$		0			0
$89$	−52.3329	−	30.2144i	−0.588010	−	0.339488i	0.176300	−	0.984336i	$-0.443587\pi$
$89$	−52.3329	−	30.2144i	−0.588010	−	0.339488i	−0.764310	+	0.644849i	$0.776920\pi$
$90$		0			0
$91$	41.7213	+	97.7639i	0.458476	+	1.07433i
$92$		0			0
$93$	−67.5345	−	38.9911i	−0.726178	−	0.419259i
$94$		0			0
$95$	−49.3972	−	18.8650i	−0.519970	−	0.198579i
$96$		0			0
$97$	−130.271			−1.34300			−0.671501	−	0.741003i	$-0.734350\pi$
$97$	−130.271			−1.34300			−0.671501	+	0.741003i	$0.734350\pi$
$98$		0			0
$99$	−154.492			−1.56053
$100$		0			0
$101$	−124.520	+	71.8914i	−1.23287	+	0.711796i	−0.967627	−	0.252386i	$-0.918785\pi$
$101$	−124.520	+	71.8914i	−1.23287	+	0.711796i	−0.265241	+	0.964182i	$0.585451\pi$
$102$		0			0
$103$	26.8014	−	46.4213i	0.260207	−	0.450692i	−0.706090	−	0.708123i	$-0.749542\pi$
$103$	26.8014	−	46.4213i	0.260207	−	0.450692i	0.966297	+	0.257430i	$0.0828757\pi$
$104$		0			0
$105$	−81.9367	+	155.463i	−0.780350	+	1.48060i
$106$		0			0
$107$	94.2108	+	54.3926i	0.880475	+	0.508342i	0.870815	−	0.491611i	$-0.163592\pi$
$107$	94.2108	+	54.3926i	0.880475	+	0.508342i	0.00965987	+	0.999953i	$0.496925\pi$
$108$		0			0
$109$	30.6519	+	53.0907i	0.281210	+	0.487071i	0.971683	−	0.236288i	$-0.0759308\pi$
$109$	30.6519	+	53.0907i	0.281210	+	0.487071i	−0.690473	+	0.723358i	$0.742597\pi$
$110$		0			0
$111$		−	98.0789i		−	0.883593i
$112$		0			0
$113$			95.2204i			0.842658i	0.906908	+	0.421329i	$0.138436\pi$
$113$			95.2204i			0.842658i	−0.906908	+	0.421329i	$0.861564\pi$
$114$		0			0
$115$	98.5037	+	37.6190i	0.856554	+	0.327122i
$116$		0			0
$117$	123.074	−	213.171i	1.05192	−	1.82197i
$118$		0			0
$119$	−98.1483	+	130.772i	−0.824775	+	1.09892i
$120$		0			0
$121$	15.0836	−	26.1255i	0.124658	−	0.215913i
$122$		0			0
$123$	164.116	−	94.7522i	1.33427	−	0.770343i
$124$		0			0
$125$	−111.083	+	57.3190i	−0.888668	+	0.458552i
$126$		0			0
$127$			116.435i			0.916812i	0.888743	+	0.458406i	$0.151580\pi$
$127$			116.435i			0.916812i	−0.888743	+	0.458406i	$0.848420\pi$
$128$		0			0
$129$	−79.3736	+	45.8263i	−0.615299	+	0.355243i
$130$		0			0
$131$	−142.914	−	82.5112i	−1.09094	−	0.629857i	−0.157116	−	0.987580i	$-0.550220\pi$
$131$	−142.914	−	82.5112i	−1.09094	−	0.629857i	−0.933828	+	0.357723i	$0.883553\pi$
$132$		0			0
$133$	8.87981	−	73.4932i	0.0667655	−	0.552580i
$134$		0			0
$135$	178.731	−	28.6214i	1.32393	−	0.212010i
$136$		0			0
$137$	−184.822	+	106.707i	−1.34907	+	0.778884i	−0.988117	−	0.153702i	$-0.950880\pi$
$137$	−184.822	+	106.707i	−1.34907	+	0.778884i	−0.360949	+	0.932586i	$0.617547\pi$
$138$		0			0
$139$			53.0872i			0.381922i	0.981598	+	0.190961i	$0.0611604\pi$
$139$			53.0872i			0.381922i	−0.981598	+	0.190961i	$0.938840\pi$
$140$		0			0
$141$	−1.55690			−0.0110418
$142$		0			0
$143$	−72.3607	−	125.332i	−0.506019	−	0.876451i
$144$		0			0
$145$	182.924	−	29.2928i	1.26155	−	0.202020i
$146$		0			0
$147$	−238.947	−	58.5970i	−1.62549	−	0.398619i
$148$		0			0
$149$	−0.00284218	+	0.00492280i	−1.90750e−5	+	3.30389e-5i	−0.866035	−	0.499983i	$-0.833339\pi$
$149$	−0.00284218	+	0.00492280i	−1.90750e−5	+	3.30389e-5i	0.866016	+	0.500017i	$0.166673\pi$
$150$		0			0
$151$	114.888	+	198.993i	0.760851	+	1.31783i	0.942412	+	0.334453i	$0.108552\pi$
$151$	114.888	+	198.993i	0.760851	+	1.31783i	−0.181562	+	0.983380i	$0.558115\pi$
$152$		0			0
$153$	378.636			2.47475
$154$		0			0
$155$	60.2669	−	48.9739i	0.388818	−	0.315961i
$156$		0			0
$157$	−22.0591	−	38.2074i	−0.140504	−	0.243360i	0.787183	−	0.616720i	$-0.211539\pi$
$157$	−22.0591	−	38.2074i	−0.140504	−	0.243360i	−0.927686	+	0.373360i	$0.878206\pi$
$158$		0			0
$159$	44.5753	+	25.7356i	0.280348	+	0.161859i
$160$		0			0
$161$	−17.7074	+	146.554i	−0.109984	+	0.910273i
$162$		0			0
$163$	−26.4560	−	15.2744i	−0.162307	−	0.0937079i	0.416646	−	0.909069i	$-0.363205\pi$
$163$	−26.4560	−	15.2744i	−0.162307	−	0.0937079i	−0.578953	+	0.815361i	$0.696539\pi$
$164$		0			0
$165$	85.3630	−	223.519i	0.517352	−	1.35466i
$166$		0			0
$167$	−102.148			−0.611665			−0.305833	−	0.952085i	$-0.598935\pi$
$167$	−102.148			−0.611665			−0.305833	+	0.952085i	$0.598935\pi$
$168$		0			0
$169$	61.5807			0.364383
$170$		0			0
$171$	−148.461	+	85.7140i	−0.868193	+	0.501251i
$172$		0			0
$173$	−136.689	+	236.753i	−0.790111	+	1.36851i	0.135787	+	0.990738i	$0.456644\pi$
$173$	−136.689	+	236.753i	−0.790111	+	1.36851i	−0.925898	+	0.377774i	$0.876689\pi$
$174$		0			0
$175$	−115.515	−	131.458i	−0.660086	−	0.751190i
$176$		0			0
$177$	15.6030	+	9.00842i	0.0881528	+	0.0508950i
$178$		0			0
$179$	−4.82428	−	8.35590i	−0.0269513	−	0.0466810i	0.852235	−	0.523159i	$-0.175247\pi$
$179$	−4.82428	−	8.35590i	−0.0269513	−	0.0466810i	−0.879186	+	0.476478i	$0.841913\pi$
$180$		0			0
$181$		−	221.537i		−	1.22396i	−0.790873	−	0.611980i	$-0.790373\pi$
$181$		−	221.537i		−	1.22396i	0.790873	−	0.611980i	$-0.209627\pi$
$182$		0			0
$183$			561.648i			3.06911i
$184$		0			0
$185$	91.2419	+	34.8457i	0.493199	+	0.188355i
$186$		0			0
$187$	111.308	−	192.792i	0.595232	−	1.03097i
$188$		0			0
$189$	99.4660	+	233.075i	0.526275	+	1.23320i
$190$		0			0
$191$	−104.905	+	181.701i	−0.549241	+	0.951313i	0.449086	+	0.893489i	$0.351750\pi$
$191$	−104.905	+	181.701i	−0.549241	+	0.951313i	−0.998327	+	0.0578244i	$0.981584\pi$
$192$		0			0
$193$	217.576	−	125.618i	1.12734	−	0.650868i	0.184073	−	0.982913i	$-0.441072\pi$
$193$	217.576	−	125.618i	1.12734	−	0.650868i	0.943264	+	0.332044i	$0.107738\pi$
$194$		0			0
$195$	240.412	+	295.848i	1.23288	+	1.51717i
$196$		0			0
$197$		−	128.792i		−	0.653768i	−0.945065	−	0.326884i	$-0.894001\pi$
$197$		−	128.792i		−	0.653768i	0.945065	−	0.326884i	$-0.105999\pi$
$198$		0			0
$199$	173.384	−	100.103i	0.871275	−	0.503031i	0.00350309	−	0.999994i	$-0.498885\pi$
$199$	173.384	−	100.103i	0.871275	−	0.503031i	0.867772	+	0.496963i	$0.165552\pi$
$200$		0			0
$201$	−55.6053	−	32.1037i	−0.276643	−	0.159720i
$202$		0			0
$203$	101.800	+	238.543i	0.501476	+	1.17509i
$204$		0			0
$205$	29.8397	+	186.339i	0.145559	+	0.908971i
$206$		0			0
$207$	296.048	−	170.924i	1.43019	−	0.825718i
$208$		0			0
$209$			100.790i			0.482249i
$210$		0			0
$211$	−167.518			−0.793924			−0.396962	−	0.917835i	$-0.629936\pi$
$211$	−167.518			−0.793924			−0.396962	+	0.917835i	$0.629936\pi$
$212$		0			0
$213$	82.3099	+	142.565i	0.386431	+	0.669319i
$214$		0			0
$215$	−14.4318	−	90.1218i	−0.0671246	−	0.419171i
$216$		0			0
$217$	86.9531	+	65.2610i	0.400706	+	0.300742i
$218$		0			0
$219$	151.397	−	262.228i	0.691312	−	1.19739i
$220$		0			0
$221$	177.345	+	307.170i	0.802465	+	1.38991i
$222$		0			0
$223$	66.6389			0.298829			0.149415	−	0.988775i	$-0.452261\pi$
$223$	66.6389			0.298829			0.149415	+	0.988775i	$0.452261\pi$
$224$		0			0
$225$	−82.9016	+	396.682i	−0.368452	+	1.76303i
$226$		0			0
$227$	−25.9245	−	44.9026i	−0.114205	−	0.197809i	0.803257	−	0.595633i	$-0.203099\pi$
$227$	−25.9245	−	44.9026i	−0.114205	−	0.197809i	−0.917462	+	0.397824i	$0.869765\pi$
$228$		0			0
$229$	63.0828	+	36.4209i	0.275471	+	0.159043i	0.631371	−	0.775481i	$-0.282492\pi$
$229$	63.0828	+	36.4209i	0.275471	+	0.159043i	−0.355900	+	0.934524i	$0.615826\pi$
$230$		0			0
$231$	332.552	+	40.1806i	1.43962	+	0.173942i
$232$		0			0
$233$	119.380	+	68.9243i	0.512362	+	0.295813i	0.733804	−	0.679361i	$-0.237743\pi$
$233$	119.380	+	68.9243i	0.512362	+	0.295813i	−0.221442	+	0.975174i	$0.571076\pi$
$234$		0			0
$235$	0.553139	−	1.44837i	0.00235378	−	0.00616327i
$236$		0			0
$237$	−458.532			−1.93473
$238$		0			0
$239$	350.640			1.46711			0.733557	−	0.679628i	$-0.237859\pi$
$239$	350.640			1.46711			0.733557	+	0.679628i	$0.237859\pi$
$240$		0			0
$241$	−264.464	+	152.688i	−1.09736	+	0.633561i	−0.935526	−	0.353257i	$-0.885074\pi$
$241$	−264.464	+	152.688i	−1.09736	+	0.633561i	−0.161833	+	0.986818i	$0.551741\pi$
$242$		0			0
$243$	−72.8405	+	126.163i	−0.299755	+	0.519191i
$244$		0			0
$245$	139.406	−	201.472i	0.569004	−	0.822334i
$246$		0			0
$247$	−139.072	−	80.2930i	−0.563043	−	0.325073i
$248$		0			0
$249$	−260.652	−	451.462i	−1.04679	−	1.81310i
$250$		0			0
$251$		−	419.508i		−	1.67135i	−0.549228	−	0.835673i	$-0.685078\pi$
$251$		−	419.508i		−	1.67135i	0.549228	−	0.835673i	$-0.314922\pi$
$252$		0			0
$253$		−	200.987i		−	0.794415i
$254$		0			0
$255$	−209.211	+	547.810i	−0.820436	+	2.14827i
$256$		0			0
$257$	3.64460	−	6.31263i	0.0141813	−	0.0245628i	−0.858848	−	0.512231i	$-0.828819\pi$
$257$	3.64460	−	6.31263i	0.0141813	−	0.0245628i	0.873029	+	0.487668i	$0.162152\pi$
$258$		0			0
$259$	−16.4020	+	135.750i	−0.0633280	+	0.524130i
$260$		0			0
$261$	300.300	−	520.135i	1.15057	−	1.99285i
$262$		0			0
$263$	118.435	−	68.3785i	0.450323	−	0.259994i	−0.257643	−	0.966240i	$-0.582946\pi$
$263$	118.435	−	68.3785i	0.450323	−	0.259994i	0.707967	+	0.706246i	$0.249613\pi$
$264$		0			0
$265$	−39.7784	+	32.3246i	−0.150107	+	0.121980i
$266$		0			0
$267$		−	303.411i		−	1.13637i
$268$		0			0
$269$	216.274	−	124.866i	0.803993	−	0.464186i	−0.0408722	−	0.999164i	$-0.513014\pi$
$269$	216.274	−	124.866i	0.803993	−	0.464186i	0.844866	+	0.534979i	$0.179680\pi$
$270$		0			0
$271$	388.441	+	224.266i	1.43336	+	0.827551i	0.997375	−	0.0724033i	$-0.0230669\pi$
$271$	388.441	+	224.266i	1.43336	+	0.827551i	0.435985	+	0.899954i	$0.356400\pi$
$272$		0			0
$273$	−320.365	+	426.851i	−1.17350	+	1.56356i
$274$		0			0
$275$	177.610	+	158.825i	0.645853	+	0.577545i
$276$		0			0
$277$	424.679	−	245.188i	1.53314	−	0.885157i	0.533922	−	0.845534i	$-0.320718\pi$
$277$	424.679	−	245.188i	1.53314	−	0.885157i	0.999215	−	0.0396228i	$-0.0126156\pi$
$278$		0			0
$279$		−	251.764i		−	0.902380i
$280$		0			0
$281$	−54.0733			−0.192432			−0.0962158	−	0.995360i	$-0.530674\pi$
$281$	−54.0733			−0.192432			−0.0962158	+	0.995360i	$0.530674\pi$
$282$		0			0
$283$	−81.2503	−	140.730i	−0.287104	−	0.497278i	0.686014	−	0.727589i	$-0.259359\pi$
$283$	−81.2503	−	140.730i	−0.287104	−	0.497278i	−0.973117	+	0.230311i	$0.926026\pi$
$284$		0			0
$285$	−41.9803	−	262.153i	−0.147299	−	0.919836i
$286$		0			0
$287$	−242.996	+	103.700i	−0.846676	+	0.361324i
$288$		0			0
$289$	−128.299	+	222.221i	−0.443942	+	0.768931i
$290$		0			0
$291$	−327.044	−	566.456i	−1.12386	−	1.94659i
$292$		0			0
$293$	298.153			1.01759			0.508794	−	0.860888i	$-0.330091\pi$
$293$	298.153			1.01759			0.508794	+	0.860888i	$0.330091\pi$
$294$		0			0
$295$	−13.9239	+	11.3148i	−0.0471998	+	0.0383553i
$296$		0			0
$297$	−172.512	−	298.800i	−0.580849	−	1.00606i
$298$		0			0
$299$	277.325	+	160.114i	0.927508	+	0.535497i
$300$		0			0
$301$	117.524	−	50.1539i	0.390444	−	0.166624i
$302$		0			0
$303$	−625.209	−	360.964i	−2.06339	−	1.19130i
$304$		0			0
$305$	−522.496	−	199.544i	−1.71310	−	0.654242i
$306$		0			0
$307$	197.369			0.642895			0.321447	−	0.946927i	$-0.395831\pi$
$307$	197.369			0.642895			0.321447	+	0.946927i	$0.395831\pi$
$308$		0			0
$309$	269.137			0.870995
$310$		0			0
$311$	−277.559	+	160.249i	−0.892474	+	0.515270i	−0.874751	−	0.484573i	$-0.838975\pi$
$311$	−277.559	+	160.249i	−0.892474	+	0.515270i	−0.0177229	+	0.999843i	$0.505642\pi$
$312$		0			0
$313$	−108.403	+	187.760i	−0.346337	+	0.599873i	−0.985596	−	0.169119i	$-0.945908\pi$
$313$	−108.403	+	187.760i	−0.346337	+	0.599873i	0.639259	+	0.768992i	$0.279241\pi$
$314$		0			0
$315$	−566.932	+	21.8639i	−1.79978	+	0.0694092i
$316$		0			0
$317$	−339.651	−	196.098i	−1.07145	−	0.618605i	−0.142876	−	0.989741i	$-0.545635\pi$
$317$	−339.651	−	196.098i	−1.07145	−	0.618605i	−0.928579	+	0.371136i	$0.878968\pi$
$318$		0			0
$319$	−176.560	−	305.810i	−0.553478	−	0.958652i
$320$		0			0
$321$			546.207i			1.70158i
$322$		0			0
$323$		−	247.020i		−	0.764769i
$324$		0			0
$325$	−360.639	+	118.543i	−1.10966	+	0.364747i
$326$		0			0
$327$	−153.902	+	266.567i	−0.470649	+	0.815188i
$328$		0			0
$329$	2.15489	+	0.260364i	0.00654981	+	0.000791380i
$330$		0			0
$331$	−171.860	+	297.670i	−0.519214	+	0.899304i	0.480537	+	0.876974i	$0.340442\pi$
$331$	−171.860	+	297.670i	−0.519214	+	0.899304i	−0.999751	+	0.0223298i	$0.992892\pi$
$332$		0			0
$333$	274.223	−	158.323i	0.823494	−	0.475444i
$334$		0			0
$335$	49.6214	−	40.3232i	0.148124	−	0.120368i
$336$		0			0
$337$			86.0226i			0.255260i	0.991822	+	0.127630i	$0.0407370\pi$
$337$			86.0226i			0.255260i	−0.991822	+	0.127630i	$0.959263\pi$
$338$		0			0
$339$	−414.045	+	239.049i	−1.22137	+	0.705159i
$340$		0			0
$341$	−128.192	−	74.0115i	−0.375929	−	0.217043i
$342$		0			0
$343$	320.925	+	121.063i	0.935641	+	0.352954i
$344$		0			0
$345$	83.7136	+	522.764i	0.242648	+	1.51526i
$346$		0			0
$347$	−531.356	+	306.778i	−1.53129	+	0.884088i	−0.531982	+	0.846756i	$0.678553\pi$
$347$	−531.356	+	306.778i	−1.53129	+	0.884088i	−0.999303	+	0.0373324i	$0.988114\pi$
$348$		0			0
$349$		−	202.068i		−	0.578990i	−0.957180	−	0.289495i	$-0.906513\pi$
$349$		−	202.068i		−	0.578990i	0.957180	−	0.289495i	$-0.0934874\pi$
$350$		0			0
$351$	549.718			1.56615
$352$		0			0
$353$	−255.952	−	443.323i	−0.725078	−	1.25587i	−0.958942	−	0.283602i	$-0.908470\pi$
$353$	−255.952	−	443.323i	−0.725078	−	1.25587i	0.233864	−	0.972269i	$-0.424863\pi$
$354$		0			0
$355$	−161.870	+	25.9213i	−0.455972	+	0.0730177i
$356$		0			0
$357$	−815.032	−	98.4762i	−2.28300	−	0.275844i
$358$		0			0
$359$	−79.2023	+	137.182i	−0.220619	+	0.382124i	−0.954996	−	0.296618i	$-0.904141\pi$
$359$	−79.2023	+	137.182i	−0.220619	+	0.382124i	0.734377	+	0.678742i	$0.237475\pi$
$360$		0			0
$361$	−124.581	−	215.780i	−0.345099	−	0.597729i
$362$		0			0
$363$	151.468			0.417268
$364$		0			0
$365$	190.159	+	234.009i	0.520985	+	0.641119i
$366$		0			0
$367$	−163.167	−	282.613i	−0.444596	−	0.770062i	0.553428	−	0.832897i	$-0.313319\pi$
$367$	−163.167	−	282.613i	−0.444596	−	0.770062i	−0.998024	+	0.0628347i	$0.979986\pi$
$368$		0			0
$369$	529.844	+	305.906i	1.43589	+	0.829013i
$370$		0			0
$371$	−57.3923	−	43.0747i	−0.154696	−	0.116104i
$372$		0			0
$373$	−252.630	−	145.856i	−0.677292	−	0.391035i	0.121542	−	0.992586i	$-0.461216\pi$
$373$	−252.630	−	145.856i	−0.677292	−	0.391035i	−0.798834	+	0.601551i	$0.794549\pi$
$374$		0			0
$375$	−528.112	−	339.124i	−1.40830	−	0.904331i
$376$		0			0
$377$	562.615			1.49235
$378$		0			0
$379$	677.228			1.78688			0.893441	−	0.449181i	$-0.148284\pi$
$379$	677.228			1.78688			0.893441	+	0.449181i	$0.148284\pi$
$380$		0			0
$381$	−506.293	+	292.309i	−1.32885	+	0.767214i
$382$		0			0
$383$	−124.602	+	215.817i	−0.325332	+	0.563491i	−0.981579	−	0.191055i	$-0.938809\pi$
$383$	−124.602	+	215.817i	−0.325332	+	0.563491i	0.656248	+	0.754545i	$0.272143\pi$
$384$		0			0
$385$	−155.530	+	295.095i	−0.403973	+	0.766479i
$386$		0			0
$387$	−256.256	−	147.950i	−0.662160	−	0.382298i
$388$		0			0
$389$	14.3803	+	24.9074i	0.0369673	+	0.0640293i	0.883917	−	0.467644i	$-0.154897\pi$
$389$	14.3803	+	24.9074i	0.0369673	+	0.0640293i	−0.846950	+	0.531673i	$0.821564\pi$
$390$		0			0
$391$			492.587i			1.25981i
$392$		0			0
$393$		−	828.572i		−	2.10833i
$394$		0			0
$395$	162.908	−	426.568i	0.412426	−	1.07992i
$396$		0			0
$397$	−126.465	+	219.043i	−0.318550	+	0.551746i	−0.980186	−	0.198080i	$-0.936529\pi$
$397$	−126.465	+	219.043i	−0.318550	+	0.551746i	0.661635	+	0.749826i	$0.269863\pi$
$398$		0			0
$399$	341.862	−	145.891i	0.856796	−	0.365643i
$400$		0			0
$401$	103.441	−	179.165i	0.257958	−	0.446796i	−0.707737	−	0.706476i	$-0.750284\pi$
$401$	103.441	−	179.165i	0.257958	−	0.446796i	0.965695	+	0.259680i	$0.0836171\pi$
$402$		0			0
$403$	204.244	−	117.921i	0.506810	−	0.292607i
$404$		0			0
$405$	113.126	+	139.213i	0.279325	+	0.343735i
$406$		0			0
$407$		−	186.170i		−	0.457420i
$408$		0			0
$409$	577.695	−	333.532i	1.41246	−	0.815483i	0.416838	−	0.908981i	$-0.363138\pi$
$409$	577.695	−	333.532i	1.41246	−	0.815483i	0.995619	+	0.0934983i	$0.0298050\pi$
$410$		0			0
$411$	−927.985	−	535.773i	−2.25787	−	1.30358i
$412$		0			0
$413$	−20.0895	−	15.0778i	−0.0486428	−	0.0365079i
$414$		0			0
$415$	512.595	−	82.0852i	1.23517	−	0.197796i
$416$		0			0
$417$	−230.838	+	133.274i	−0.553569	+	0.319603i
$418$		0			0
$419$		−	82.9914i		−	0.198070i	−0.995084	−	0.0990350i	$-0.968424\pi$
$419$		−	82.9914i		−	0.198070i	0.995084	−	0.0990350i	$-0.0315756\pi$
$420$		0			0
$421$	155.483			0.369319			0.184659	−	0.982803i	$-0.440882\pi$
$421$	155.483			0.369319			0.184659	+	0.982803i	$0.440882\pi$
$422$		0			0
$423$	−2.51321	−	4.35301i	−0.00594140	−	0.0102908i
$424$		0			0
$425$	−435.293	−	389.254i	−1.02422	−	0.915893i
$426$		0			0
$427$	93.9257	−	777.370i	0.219967	−	1.82054i
$428$		0			0
$429$	363.321	−	629.290i	0.846901	−	1.46688i
$430$		0			0
$431$	−17.6114	−	30.5039i	−0.0408618	−	0.0707748i	0.844871	−	0.534970i	$-0.179677\pi$
$431$	−17.6114	−	30.5039i	−0.0408618	−	0.0707748i	−0.885733	+	0.464195i	$0.846344\pi$
$432$		0			0
$433$	98.0262			0.226388			0.113194	−	0.993573i	$-0.463892\pi$
$433$	98.0262			0.226388			0.113194	+	0.993573i	$0.463892\pi$
$434$		0			0
$435$	586.602	+	721.867i	1.34851	+	1.65947i
$436$		0			0
$437$	−111.510	−	193.141i	−0.255171	−	0.441969i
$438$		0			0
$439$	−356.391	−	205.763i	−0.811826	−	0.468708i	0.0357638	−	0.999360i	$-0.488614\pi$
$439$	−356.391	−	205.763i	−0.811826	−	0.468708i	−0.847589	+	0.530653i	$0.821947\pi$
$440$		0			0
$441$	−221.884	−	762.674i	−0.503139	−	1.72942i
$442$		0			0
$443$	656.457	+	379.006i	1.48184	+	0.855543i	0.999788	−	0.0205969i	$-0.00655665\pi$
$443$	656.457	+	379.006i	1.48184	+	0.855543i	0.482057	+	0.876140i	$0.339890\pi$
$444$		0			0
$445$	282.260	+	107.797i	0.634293	+	0.242239i
$446$		0			0
$447$	−0.0285410			−6.38500e−5
$448$		0			0
$449$	−49.9480			−0.111243			−0.0556213	−	0.998452i	$-0.517714\pi$
$449$	−49.9480			−0.111243			−0.0556213	+	0.998452i	$0.517714\pi$
$450$		0			0
$451$	311.519	−	179.855i	0.690729	−	0.398792i
$452$		0			0
$453$	−576.851	+	999.135i	−1.27340	+	2.20560i
$454$		0			0
$455$	−283.275	−	449.685i	−0.622583	−	0.988318i
$456$		0			0
$457$	350.458	+	202.337i	0.766866	+	0.442750i	0.831755	−	0.555142i	$-0.187336\pi$
$457$	350.458	+	202.337i	0.766866	+	0.442750i	−0.0648896	+	0.997892i	$0.520670\pi$
$458$		0			0
$459$	422.800	+	732.311i	0.921133	+	1.59545i
$460$		0			0
$461$		−	41.4395i		−	0.0898904i	−0.998989	−	0.0449452i	$-0.985689\pi$
$461$		−	41.4395i		−	0.0898904i	0.998989	−	0.0449452i	$-0.0143113\pi$
$462$		0			0
$463$		−	668.770i		−	1.44443i	−0.691670	−	0.722213i	$-0.743125\pi$
$463$		−	668.770i		−	1.44443i	0.691670	−	0.722213i	$-0.256875\pi$
$464$		0			0
$465$	364.251	+	139.109i	0.783336	+	0.299160i
$466$		0			0
$467$	−248.677	+	430.721i	−0.532498	+	0.922314i	0.466782	+	0.884373i	$0.345413\pi$
$467$	−248.677	+	430.721i	−0.532498	+	0.922314i	−0.999280	+	0.0379417i	$0.987920\pi$
$468$		0			0
$469$	71.5939	+	53.7334i	0.152652	+	0.114570i
$470$		0			0
$471$	110.758	−	191.838i	0.235155	−	0.407300i
$472$		0			0
$473$	−150.664	+	86.9860i	−0.318529	+	0.183903i
$474$		0			0
$475$	258.793	+	54.0846i	0.544828	+	0.113862i
$476$		0			0
$477$			166.174i			0.348372i
$478$		0			0
$479$	−383.598	+	221.470i	−0.800830	+	0.462360i	−0.843761	−	0.536718i	$-0.819664\pi$
$479$	−383.598	+	221.470i	−0.800830	+	0.462360i	0.0429311	+	0.999078i	$0.486330\pi$
$480$		0			0
$481$	256.880	+	148.310i	0.534054	+	0.308336i
$482$		0			0
$483$	−681.712	+	290.924i	−1.41141	+	0.602328i
$484$		0			0
$485$	643.162	−	102.994i	1.32611	−	0.212358i
$486$		0			0
$487$	97.2891	−	56.1699i	0.199772	−	0.115339i	−0.396777	−	0.917915i	$-0.629871\pi$
$487$	97.2891	−	56.1699i	0.199772	−	0.115339i	0.596549	+	0.802576i	$0.296538\pi$
$488$		0			0
$489$		−	153.384i		−	0.313670i
$490$		0			0
$491$	677.177			1.37918			0.689590	−	0.724200i	$-0.257791\pi$
$491$	677.177			1.37918			0.689590	+	0.724200i	$0.257791\pi$
$492$		0			0
$493$	432.719	+	749.492i	0.877727	+	1.52027i
$494$		0			0
$495$	762.744	−	122.143i	1.54090	−	0.246754i
$496$		0			0
$497$	−90.0826	−	211.087i	−0.181253	−	0.424723i
$498$		0			0
$499$	461.215	−	798.848i	0.924279	−	1.60090i	0.131562	−	0.991308i	$-0.458001\pi$
$499$	461.215	−	798.848i	0.924279	−	1.60090i	0.792717	−	0.609590i	$-0.208666\pi$
$500$		0			0
$501$	−256.441	−	444.169i	−0.511858	−	0.886564i
$502$		0			0
$503$	136.712			0.271793			0.135896	−	0.990723i	$-0.456609\pi$
$503$	136.712			0.271793			0.135896	+	0.990723i	$0.456609\pi$
$504$		0			0
$505$	557.927	−	453.381i	1.10481	−	0.897785i
$506$		0			0
$507$	154.597	+	267.770i	0.304925	+	0.528146i
$508$		0			0
$509$	−619.262	−	357.531i	−1.21662	−	0.702418i	−0.252430	−	0.967615i	$-0.581230\pi$
$509$	−619.262	−	357.531i	−1.21662	−	0.702418i	−0.964194	+	0.265197i	$0.914563\pi$
$510$		0			0
$511$	−253.400	+	337.628i	−0.495891	+	0.660720i
$512$		0			0
$513$	−331.554	−	191.423i	−0.646305	−	0.373144i
$514$		0			0
$515$	−95.6198	+	250.376i	−0.185670	+	0.486167i
$516$		0			0
$517$	−2.95525			−0.00571616
$518$		0			0
$519$	−1372.62			−2.64475
$520$		0			0
$521$	14.6765	−	8.47346i	0.0281698	−	0.0162638i	−0.485849	−	0.874043i	$-0.661490\pi$
$521$	14.6765	−	8.47346i	0.0281698	−	0.0162638i	0.514019	+	0.857779i	$0.328156\pi$
$522$		0			0
$523$	−351.622	+	609.027i	−0.672317	+	1.16449i	0.304928	+	0.952375i	$0.401368\pi$
$523$	−351.622	+	609.027i	−0.672317	+	1.16449i	−0.977245	+	0.212113i	$0.931966\pi$
$524$		0			0
$525$	281.619	−	832.316i	0.536418	−	1.58536i
$526$		0			0
$527$	314.178	+	181.391i	0.596162	+	0.344195i
$528$		0			0
$529$	−42.1366	−	72.9828i	−0.0796533	−	0.137964i
$530$		0			0
$531$			58.1670i			0.109542i
$532$		0			0
$533$			573.117i			1.07527i
$534$		0			0
$535$	−508.131	−	194.058i	−0.949778	−	0.362725i
$536$		0			0
$537$	24.2225	−	41.9547i	0.0451071	−	0.0781279i
$538$		0			0
$539$	−453.562	−	111.227i	−0.841488	−	0.206358i
$540$		0			0
$541$	−473.725	+	820.515i	−0.875647	+	1.51666i	−0.0195742	+	0.999808i	$0.506231\pi$
$541$	−473.725	+	820.515i	−0.875647	+	1.51666i	−0.856072	+	0.516856i	$0.827102\pi$
$542$		0			0
$543$	963.305	−	556.165i	1.77404	−	1.02424i
$544$		0			0
$545$	−193.306	−	237.880i	−0.354689	−	0.436478i
$546$		0			0
$547$			451.960i			0.826252i	0.910674	+	0.413126i	$0.135563\pi$
$547$			451.960i			0.826252i	−0.910674	+	0.413126i	$0.864437\pi$
$548$		0			0
$549$	−1570.34	+	906.635i	−2.86036	+	1.65143i
$550$		0			0
$551$	−339.333	−	195.914i	−0.615850	−	0.355561i
$552$		0			0
$553$	634.648	+	76.6814i	1.14765	+	0.138664i
$554$		0			0
$555$	77.5421	+	484.225i	0.139715	+	0.872478i
$556$		0			0
$557$	331.417	−	191.344i	0.595004	−	0.343526i	−0.172069	−	0.985085i	$-0.555045\pi$
$557$	331.417	−	191.344i	0.595004	−	0.343526i	0.767074	+	0.641559i	$0.221712\pi$
$558$		0			0
$559$		−	277.185i		−	0.495858i
$560$		0			0
$561$	1117.75			1.99243
$562$		0			0
$563$	−22.9940	−	39.8268i	−0.0408419	−	0.0707402i	0.844882	−	0.534953i	$-0.179671\pi$
$563$	−22.9940	−	39.8268i	−0.0408419	−	0.0707402i	−0.885724	+	0.464213i	$0.846337\pi$
$564$		0			0
$565$	−75.2821	−	470.112i	−0.133243	−	0.832057i
$566$		0			0
$567$	−150.749	+	200.856i	−0.265871	+	0.354244i
$568$		0			0
$569$	15.4807	−	26.8133i	0.0272068	−	0.0471236i	−0.852101	−	0.523377i	$-0.824672\pi$
$569$	15.4807	−	26.8133i	0.0272068	−	0.0471236i	0.879308	+	0.476253i	$0.158005\pi$
$570$		0			0
$571$	200.579	+	347.414i	0.351277	+	0.608430i	0.986474	−	0.163921i	$-0.0524141\pi$
$571$	200.579	+	347.414i	0.351277	+	0.608430i	−0.635196	+	0.772351i	$0.719081\pi$
$572$		0			0
$573$	−1053.45			−1.83848
$574$		0			0
$575$	−516.064	−	107.851i	−0.897503	−	0.187567i
$576$		0			0
$577$	−388.494	−	672.891i	−0.673300	−	1.16619i	−0.976963	−	0.213410i	$-0.931543\pi$
$577$	−388.494	−	672.891i	−0.673300	−	1.16619i	0.303663	−	0.952780i	$-0.401790\pi$
$578$		0			0
$579$	1092.44	+	630.722i	1.88677	+	1.08933i
$580$		0			0
$581$	285.266	+	668.452i	0.490991	+	1.15052i
$582$		0			0
$583$	84.6114	+	48.8504i	0.145131	+	0.0837914i
$584$		0			0
$585$	−439.095	+	1149.75i	−0.750589	+	1.96538i
$586$		0			0
$587$	123.033			0.209596			0.104798	−	0.994494i	$-0.466580\pi$
$587$	123.033			0.209596			0.104798	+	0.994494i	$0.466580\pi$
$588$		0			0
$589$	−164.249			−0.278862
$590$		0			0
$591$	560.025	−	323.331i	0.947589	−	0.547091i
$592$		0			0
$593$	211.024	−	365.504i	0.355858	−	0.616364i	−0.631407	−	0.775452i	$-0.717522\pi$
$593$	211.024	−	365.504i	0.355858	−	0.616364i	0.987264	+	0.159088i	$0.0508554\pi$
$594$		0			0
$595$	381.178	−	723.230i	0.640636	−	1.21551i
$596$		0			0
$597$	870.553	+	502.614i	1.45821	+	0.841900i
$598$		0			0
$599$	−414.355	−	717.684i	−0.691745	−	1.19814i	−0.971266	−	0.237998i	$-0.923509\pi$
$599$	−414.355	−	717.684i	−0.691745	−	1.19814i	0.279521	−	0.960140i	$-0.409824\pi$
$600$		0			0
$601$			675.102i			1.12330i	0.827376	+	0.561649i	$0.189833\pi$
$601$			675.102i			1.12330i	−0.827376	+	0.561649i	$0.810167\pi$
$602$		0			0
$603$		−	207.293i		−	0.343769i
$604$		0			0
$605$	−53.8140	+	140.909i	−0.0889487	+	0.232908i
$606$		0			0
$607$	491.492	−	851.289i	0.809707	−	1.40245i	−0.103360	−	0.994644i	$-0.532959\pi$
$607$	491.492	−	851.289i	0.809707	−	1.40245i	0.913067	−	0.407809i	$-0.133707\pi$
$608$		0			0
$609$	−781.687	+	1041.51i	−1.28356	+	1.71020i
$610$		0			0
$611$	2.35426	−	4.07770i	0.00385313	−	0.00667382i
$612$		0			0
$613$	418.163	−	241.427i	0.682159	−	0.393844i	−0.118509	−	0.992953i	$-0.537812\pi$
$613$	418.163	−	241.427i	0.682159	−	0.393844i	0.800668	+	0.599108i	$0.204478\pi$
$614$		0			0
$615$	−735.343	+	597.552i	−1.19568	+	0.971630i
$616$		0			0
$617$			550.193i			0.891722i	0.895102	+	0.445861i	$0.147103\pi$
$617$			550.193i			0.891722i	−0.895102	+	0.445861i	$0.852897\pi$
$618$		0			0
$619$	−535.910	+	309.408i	−0.865767	+	0.499851i	−0.865939	−	0.500149i	$-0.833279\pi$
$619$	−535.910	+	309.408i	−0.865767	+	0.499851i	0.000172089		1.00000i	$0.499945\pi$
$620$		0			0
$621$	661.158	+	381.720i	1.06467	+	0.614686i
$622$		0			0
$623$	−50.7401	+	419.947i	−0.0814448	+	0.674073i
$624$		0			0
$625$	503.113	−	370.813i	0.804981	−	0.593301i
$626$		0			0
$627$	−438.264	+	253.032i	−0.698985	+	0.403559i
$628$		0			0
$629$			456.273i			0.725395i
$630$		0			0
$631$	167.847			0.266001			0.133000	−	0.991116i	$-0.457539\pi$
$631$	167.847			0.266001			0.133000	+	0.991116i	$0.457539\pi$
$632$		0			0
$633$	−420.551	−	728.416i	−0.664378	−	1.15074i
$634$		0			0
$635$	−92.0547	−	574.852i	−0.144968	−	0.905279i
$636$		0			0
$637$	514.796	−	537.224i	0.808157	−	0.843365i
$638$		0			0
$639$	−265.736	+	460.268i	−0.415862	+	0.720294i
$640$		0			0
$641$	−529.087	−	916.406i	−0.825409	−	1.42965i	−0.901606	−	0.432558i	$-0.857611\pi$
$641$	−529.087	−	916.406i	−0.825409	−	1.42965i	0.0761967	−	0.997093i	$-0.475722\pi$
$642$		0			0
$643$	68.2597			0.106158			0.0530791	−	0.998590i	$-0.483096\pi$
$643$	68.2597			0.106158			0.0530791	+	0.998590i	$0.483096\pi$
$644$		0			0
$645$	355.644	−	289.003i	0.551387	−	0.448066i
$646$		0			0
$647$	−26.7770	−	46.3792i	−0.0413865	−	0.0716835i	0.844590	−	0.535413i	$-0.179844\pi$
$647$	−26.7770	−	46.3792i	−0.0413865	−	0.0716835i	−0.885977	+	0.463730i	$0.846511\pi$
$648$		0			0
$649$	29.6172	+	17.0995i	0.0456351	+	0.0263474i
$650$		0			0
$651$	−65.4791	+	541.934i	−0.100582	+	0.832463i
$652$		0			0
$653$	39.7204	+	22.9326i	0.0608276	+	0.0351188i	0.530105	−	0.847932i	$-0.322152\pi$
$653$	39.7204	+	22.9326i	0.0608276	+	0.0351188i	−0.469278	+	0.883051i	$0.655486\pi$
$654$		0			0
$655$	770.813	+	294.377i	1.17681	+	0.449431i
$656$		0			0
$657$	977.567			1.48793
$658$		0			0
$659$	−997.845			−1.51418			−0.757090	−	0.653310i	$-0.773380\pi$
$659$	−997.845			−1.51418			−0.757090	+	0.653310i	$0.773380\pi$
$660$		0			0
$661$	229.919	−	132.744i	0.347836	−	0.200823i	−0.315896	−	0.948794i	$-0.602305\pi$
$661$	229.919	−	132.744i	0.347836	−	0.200823i	0.663732	+	0.747971i	$0.268972\pi$
$662$		0			0
$663$	−890.441	+	1542.29i	−1.34305	+	2.32623i
$664$		0			0
$665$	14.2639	+	369.863i	0.0214495	+	0.556186i
$666$		0			0
$667$	676.670	+	390.676i	1.01450	+	0.585720i
$668$		0			0
$669$	167.296	+	289.765i	0.250069	+	0.433131i
$670$		0			0
$671$			1066.10i			1.58882i
$672$		0			0
$673$		−	859.611i		−	1.27728i	−0.769505	−	0.638641i	$-0.779497\pi$
$673$		−	859.611i		−	1.27728i	0.769505	−	0.638641i	$-0.220503\pi$
$674$		0			0
$675$	−859.784	+	282.613i	−1.27375	+	0.418686i
$676$		0			0
$677$	35.7345	−	61.8940i	0.0527836	−	0.0914239i	−0.838426	−	0.545015i	$-0.816524\pi$
$677$	35.7345	−	61.8940i	0.0527836	−	0.0914239i	0.891210	+	0.453591i	$0.149857\pi$
$678$		0			0
$679$	357.927	+	838.718i	0.527139	+	1.23522i
$680$		0			0
$681$	130.166	−	225.454i	0.191140	−	0.331064i
$682$		0			0
$683$	832.644	−	480.727i	1.21910	−	0.703847i	0.254373	−	0.967106i	$-0.418131\pi$
$683$	832.644	−	480.727i	1.21910	−	0.703847i	0.964725	+	0.263259i	$0.0847975\pi$
$684$		0			0
$685$	828.121	−	672.945i	1.20894	−	0.982402i
$686$		0			0
$687$			365.736i			0.532367i
$688$		0			0
$689$	−134.809	+	77.8320i	−0.195659	+	0.112964i
$690$		0			0
$691$	−433.591	−	250.334i	−0.627483	−	0.362277i	0.152294	−	0.988335i	$-0.451334\pi$
$691$	−433.591	−	250.334i	−0.627483	−	0.362277i	−0.779777	+	0.626058i	$0.784667\pi$
$692$		0			0
$693$	424.476	+	994.659i	0.612520	+	1.43529i
$694$		0			0
$695$	−41.9712	−	262.097i	−0.0603903	−	0.377117i
$696$		0			0
$697$	−763.483	+	440.797i	−1.09538	+	0.632420i
$698$		0			0
$699$			692.133i			0.990176i
$700$		0			0
$701$	−913.148			−1.30264			−0.651318	−	0.758805i	$-0.725784\pi$
$701$	−913.148			−1.30264			−0.651318	+	0.758805i	$0.725784\pi$
$702$		0			0
$703$	−103.289	−	178.902i	−0.146926	−	0.254484i
$704$		0			0
$705$	7.68657	−	1.23090i	0.0109029	−	0.00174596i
$706$		0			0
$707$	804.979	+	604.161i	1.13858	+	0.854542i
$708$		0			0
$709$	−573.474	+	993.286i	−0.808849	+	1.40097i	0.104812	+	0.994492i	$0.466576\pi$
$709$	−573.474	+	993.286i	−0.808849	+	1.40097i	−0.913661	+	0.406476i	$0.866757\pi$
$710$		0			0
$711$	−740.181	−	1282.03i	−1.04104	−	1.80314i
$712$		0			0
$713$	327.533			0.459373
$714$		0			0
$715$	456.341	+	561.570i	0.638239	+	0.785412i
$716$		0			0
$717$	880.277	+	1524.68i	1.22772	+	2.12648i
$718$		0			0
$719$	84.0179	+	48.5077i	0.116854	+	0.0674656i	0.557288	−	0.830319i	$-0.311842\pi$
$719$	84.0179	+	48.5077i	0.116854	+	0.0674656i	−0.440434	+	0.897785i	$0.645175\pi$
$720$		0			0
$721$	−372.510	−	45.0085i	−0.516657	−	0.0624251i
$722$		0			0
$723$	−1327.86	−	766.642i	−1.83660	−	1.06036i
$724$		0			0
$725$	−879.956	+	289.243i	−1.21373	+	0.398956i
$726$		0			0
$727$	−175.776			−0.241782			−0.120891	−	0.992666i	$-0.538575\pi$
$727$	−175.776			−0.241782			−0.120891	+	0.992666i	$0.538575\pi$
$728$		0			0
$729$	−1054.35			−1.44629
$730$		0			0
$731$	369.254	−	213.189i	0.505136	−	0.291640i
$732$		0			0
$733$	−346.840	+	600.745i	−0.473179	+	0.819570i	−0.999529	−	0.0306981i	$-0.990227\pi$
$733$	−346.840	+	600.745i	−0.473179	+	0.819570i	0.526350	+	0.850268i	$0.323560\pi$
$734$		0			0
$735$	1226.03	+	100.385i	1.66807	+	0.136579i
$736$		0			0
$737$	−105.548	−	60.9383i	−0.143213	−	0.0826842i
$738$		0			0
$739$	10.2585	+	17.7682i	0.0138816	+	0.0240436i	0.872883	−	0.487930i	$-0.162248\pi$
$739$	10.2585	+	17.7682i	0.0138816	+	0.0240436i	−0.859001	+	0.511974i	$0.828915\pi$
$740$		0			0
$741$		−	806.296i		−	1.08812i
$742$		0			0
$743$		−	896.676i		−	1.20683i	−0.797427	−	0.603416i	$-0.793806\pi$
$743$		−	896.676i		−	1.20683i	0.797427	−	0.603416i	$-0.206194\pi$
$744$		0			0
$745$	0.0101401	−	0.0265514i	1.36109e−5	−	3.56394e-5i
$746$		0			0
$747$	841.509	−	1457.54i	1.12652	−	1.95119i
$748$		0			0
$749$	91.3435	−	755.999i	0.121954	−	1.00934i
$750$		0			0
$751$	−298.227	+	516.545i	−0.397107	+	0.687809i	−0.993368	−	0.114982i	$-0.963319\pi$
$751$	−298.227	+	516.545i	−0.397107	+	0.687809i	0.596261	+	0.802791i	$0.296652\pi$
$752$		0			0
$753$	1824.14	−	1053.17i	2.42249	−	1.39863i
$754$		0			0
$755$	−724.541	−	891.615i	−0.959657	−	1.18095i
$756$		0			0
$757$		−	118.056i		−	0.155952i	−0.996955	−	0.0779761i	$-0.975154\pi$
$757$		−	118.056i		−	0.155952i	0.996955	−	0.0779761i	$-0.0248458\pi$
$758$		0			0
$759$	873.949	−	504.575i	1.15145	−	0.664789i
$760$		0			0
$761$	695.093	+	401.312i	0.913395	+	0.527349i	0.881522	−	0.472143i	$-0.156520\pi$
$761$	695.093	+	401.312i	0.913395	+	0.527349i	0.0318728	+	0.999492i	$0.489853\pi$
$762$		0			0
$763$	257.593	−	343.214i	0.337605	−	0.449822i
$764$		0			0
$765$	−1869.36	+	299.353i	−2.44361	+	0.391312i
$766$		0			0
$767$	−47.1882	+	27.2441i	−0.0615231	+	0.0355204i
$768$		0			0
$769$		−	1022.31i		−	1.32940i	−0.747109	−	0.664701i	$-0.768559\pi$
$769$		−	1022.31i		−	1.32940i	0.747109	−	0.664701i	$-0.231441\pi$
$770$		0			0
$771$	36.5988			0.0474693
$772$		0			0
$773$	−343.943	−	595.726i	−0.444945	−	0.770668i	0.553103	−	0.833113i	$-0.313444\pi$
$773$	−343.943	−	595.726i	−0.444945	−	0.770668i	−0.998048	+	0.0624449i	$0.980110\pi$
$774$		0			0
$775$	−258.824	+	289.436i	−0.333967	+	0.373466i
$776$		0			0
$777$	−631.455	+	269.477i	−0.812684	+	0.346817i
$778$		0			0
$779$	199.571	−	345.668i	0.256189	−	0.443733i
$780$		0			0
$781$	156.238	+	270.612i	0.200048	+	0.346494i
$782$		0			0
$783$	1341.31			1.71303
$784$		0			0
$785$	139.115	+	171.194i	0.177217	+	0.218081i
$786$		0			0
$787$	612.772	+	1061.35i	0.778618	+	1.34861i	0.932739	+	0.360553i	$0.117412\pi$
$787$	612.772	+	1061.35i	0.778618	+	1.34861i	−0.154121	+	0.988052i	$0.549255\pi$
$788$		0			0
$789$	594.658	+	343.326i	0.753686	+	0.435141i
$790$		0			0
$791$	613.052	−	261.623i	0.775034	−	0.330750i
$792$		0			0
$793$	−1471.02	−	849.295i	−1.85501	−	1.07099i
$794$		0			0
$795$	−240.420	−	91.8174i	−0.302414	−	0.115494i
$796$		0			0
$797$	−691.172			−0.867217			−0.433608	−	0.901101i	$-0.642760\pi$
$797$	−691.172			−0.867217			−0.433608	+	0.901101i	$0.642760\pi$
$798$		0			0
$799$	7.24286			0.00906491
$800$		0			0
$801$	848.321	−	489.778i	1.05908	−	0.611458i
$802$		0			0
$803$	287.377	−	497.752i	0.357880	−	0.619866i
$804$		0			0
$805$	−28.4439	−	737.551i	−0.0353340	−	0.916212i
$806$		0			0
$807$	1085.91	+	626.948i	1.34561	+	0.776887i
$808$		0			0
$809$	511.628	+	886.165i	0.632420	+	1.09538i	0.987056	+	0.160379i	$0.0512716\pi$
$809$	511.628	+	886.165i	0.632420	+	1.09538i	−0.354636	+	0.935005i	$0.615395\pi$
$810$		0			0
$811$		−	346.588i		−	0.427359i	−0.976904	−	0.213679i	$-0.931455\pi$
$811$		−	346.588i		−	0.427359i	0.976904	−	0.213679i	$-0.0685448\pi$
$812$		0			0
$813$			2252.07i			2.77007i
$814$		0			0
$815$	142.692	+	54.4948i	0.175082	+	0.0668648i
$816$		0			0
$817$	−96.5215	+	167.180i	−0.118141	+	0.204627i
$818$		0			0
$819$	−1710.60	−	206.683i	−2.08864	−	0.252360i
$820$		0			0
$821$	302.304	−	523.605i	0.368214	−	0.637765i	−0.621072	−	0.783753i	$-0.713303\pi$
$821$	302.304	−	523.605i	0.368214	−	0.637765i	0.989286	+	0.145988i	$0.0466360\pi$
$822$		0			0
$823$	−1002.77	+	578.951i	−1.21844	+	0.703464i	−0.964583	−	0.263779i	$-0.915031\pi$
$823$	−1002.77	+	578.951i	−1.21844	+	0.703464i	−0.253853	+	0.967243i	$0.581698\pi$
$824$		0			0
$825$	−244.729	+	1171.02i	−0.296642	+	1.41942i
$826$		0			0
$827$			248.293i			0.300234i	0.988668	+	0.150117i	$0.0479650\pi$
$827$			248.293i			0.300234i	−0.988668	+	0.150117i	$0.952035\pi$
$828$		0			0
$829$	808.027	−	466.515i	0.974701	−	0.562744i	0.0740349	−	0.997256i	$-0.476412\pi$
$829$	808.027	−	466.515i	0.974701	−	0.562744i	0.900666	+	0.434512i	$0.143079\pi$
$830$		0			0
$831$	2132.30	+	1231.08i	2.56594	+	1.48145i
$832$		0			0
$833$	1111.61	+	272.600i	1.33446	+	0.327250i
$834$		0			0
$835$	504.315	−	80.7592i	0.603970	−	0.0967176i
$836$		0			0
$837$	486.930	−	281.129i	0.581757	−	0.335877i
$838$		0			0
$839$		−	1426.14i		−	1.69981i	−0.526934	−	0.849906i	$-0.676659\pi$
$839$		−	1426.14i		−	1.69981i	0.526934	−	0.849906i	$-0.323341\pi$
$840$		0			0
$841$	531.775			0.632312
$842$		0			0
$843$	−135.750	−	235.126i	−0.161032	−	0.278916i
$844$		0			0
$845$	−304.030	+	48.6862i	−0.359798	+	0.0576169i
$846$		0			0
$847$	−209.645	−	25.3304i	−0.247515	−	0.0299060i
$848$		0			0
$849$	407.955	−	706.599i	0.480512	−	0.832272i
$850$		0			0
$851$	205.970	+	356.751i	0.242033	+	0.419214i
$852$		0			0
$853$	350.268			0.410631			0.205315	−	0.978696i	$-0.434178\pi$
$853$	350.268			0.410631			0.205315	+	0.978696i	$0.434178\pi$
$854$		0			0
$855$	665.200	−	540.553i	0.778012	−	0.632226i
$856$		0			0
$857$	−15.1063	−	26.1649i	−0.0176269	−	0.0305308i	0.857077	−	0.515188i	$-0.172278\pi$
$857$	−15.1063	−	26.1649i	−0.0176269	−	0.0305308i	−0.874704	+	0.484657i	$0.838944\pi$
$858$		0			0
$859$	−370.864	−	214.119i	−0.431740	−	0.249265i	0.268348	−	0.963322i	$-0.413522\pi$
$859$	−370.864	−	214.119i	−0.431740	−	0.249265i	−0.700087	+	0.714057i	$0.746856\pi$
$860$		0			0
$861$	−1060.95	−	796.279i	−1.23223	−	0.924830i
$862$		0			0
$863$	−1021.22	−	589.602i	−1.18334	−	0.683200i	−0.226553	−	0.973999i	$-0.572746\pi$
$863$	−1021.22	−	589.602i	−1.18334	−	0.683200i	−0.956784	+	0.290798i	$0.906079\pi$
$864$		0			0
$865$	487.669	−	1276.94i	0.563779	−	1.47623i
$866$		0			0
$867$	−1288.37			−1.48601
$868$		0			0
$869$	−870.370			−1.00158
$870$		0			0
$871$	168.167	−	97.0912i	0.193073	−	0.111471i
$872$		0			0
$873$	1055.85	−	1828.79i	1.20946	−	2.09484i
$874$		0			0
$875$	674.241	+	557.695i	0.770561	+	0.637366i
$876$		0			0
$877$	1423.08	+	821.617i	1.62267	+	0.936850i	0.986202	+	0.165548i	$0.0529393\pi$
$877$	1423.08	+	821.617i	1.62267	+	0.936850i	0.636470	+	0.771302i	$0.280394\pi$
$878$		0			0
$879$	748.509	+	1296.45i	0.851546	+	1.47492i
$880$		0			0
$881$			571.268i			0.648431i	0.945983	+	0.324216i	$0.105100\pi$
$881$			571.268i			0.648431i	−0.945983	+	0.324216i	$0.894900\pi$
$882$		0			0
$883$		−	13.3627i		−	0.0151333i	−0.999971	−	0.00756666i	$-0.997591\pi$
$883$		−	13.3627i		−	0.0151333i	0.999971	−	0.00756666i	$-0.00240856\pi$
$884$		0			0
$885$	−84.1559	−	32.1395i	−0.0950914	−	0.0363159i
$886$		0			0
$887$	−662.731	+	1147.88i	−0.747160	+	1.29412i	0.202018	+	0.979382i	$0.435250\pi$
$887$	−662.731	+	1147.88i	−0.747160	+	1.29412i	−0.949179	+	0.314738i	$0.898083\pi$
$888$		0			0
$889$	749.638	−	319.912i	0.843237	−	0.359856i
$890$		0			0
$891$	170.962	−	296.115i	0.191876	−	0.332340i
$892$		0			0
$893$	−2.83988	+	1.63961i	−0.00318016	+	0.00183607i
$894$		0			0
$895$	30.4242	+	37.4398i	0.0339935	+	0.0418321i
$896$		0			0
$897$			1607.85i			1.79247i
$898$		0			0
$899$	498.354	−	287.725i	0.554343	−	0.320050i
$900$		0			0
$901$	−207.369	−	119.725i	−0.230154	−	0.132880i
$902$		0			0
$903$	513.124	+	385.116i	0.568244	+	0.426485i
$904$		0			0
$905$	175.149	+	1093.75i	0.193535	+	1.20856i
$906$		0			0
$907$	417.494	−	241.041i	0.460303	−	0.265756i	−0.251869	−	0.967761i	$-0.581045\pi$
$907$	417.494	−	241.041i	0.460303	−	0.265756i	0.712171	+	0.702006i	$0.247712\pi$
$908$		0			0
$909$		−	2330.73i		−	2.56406i
$910$		0			0
$911$	−1582.96			−1.73761			−0.868806	−	0.495153i	$-0.835112\pi$
$911$	−1582.96			−1.73761			−0.868806	+	0.495153i	$0.835112\pi$
$912$		0			0
$913$	−494.760	−	856.949i	−0.541906	−	0.938608i
$914$		0			0
$915$	−444.044	−	2772.91i	−0.485294	−	3.03050i
$916$		0			0
$917$	−138.564	+	1146.82i	−0.151106	+	1.25062i
$918$		0			0
$919$	−669.468	+	1159.55i	−0.728474	+	1.26175i	0.229054	+	0.973414i	$0.426437\pi$
$919$	−669.468	+	1159.55i	−0.728474	+	1.26175i	−0.957528	+	0.288340i	$0.906897\pi$
$920$		0			0
$921$	495.491	+	858.215i	0.537992	+	0.931830i
$922$		0			0
$923$	−497.859			−0.539392
$924$		0			0
$925$	−478.019	−	99.9000i	−0.516778	−	0.108000i
$926$		0			0
$927$	434.453	+	752.494i	0.468665	+	0.811752i
$928$		0			0
$929$	641.135	+	370.159i	0.690135	+	0.398449i	0.803662	−	0.595085i	$-0.202882\pi$
$929$	641.135	+	370.159i	0.690135	+	0.398449i	−0.113528	+	0.993535i	$0.536215\pi$
$930$		0			0
$931$	−497.564	+	144.756i	−0.534441	+	0.155485i
$932$		0			0
$933$	−1393.62	−	804.604i	−1.49369	−	0.862384i
$934$		0			0
$935$	−397.118	+	1039.83i	−0.424725	+	1.11212i
$936$		0			0
$937$	−272.107			−0.290402			−0.145201	−	0.989402i	$-0.546383\pi$
$937$	−272.107			−0.290402			−0.145201	+	0.989402i	$0.546383\pi$
$938$		0			0
$939$	−1088.58			−1.15930
$940$		0			0
$941$	203.843	−	117.689i	0.216623	−	0.125068i	−0.387762	−	0.921759i	$-0.626752\pi$
$941$	203.843	−	117.689i	0.216623	−	0.125068i	0.604386	+	0.796692i	$0.293419\pi$
$942$		0			0
$943$	−397.968	+	689.302i	−0.422024	+	0.730967i
$944$		0			0
$945$	−675.344	−	1072.07i	−0.714650	−	1.13447i
$946$		0			0
$947$	−526.514	−	303.983i	−0.555981	−	0.320996i	0.195550	−	0.980694i	$-0.437351\pi$
$947$	−526.514	−	303.983i	−0.555981	−	0.320996i	−0.751531	+	0.659698i	$0.770684\pi$
$948$		0			0
$949$	457.870	+	793.055i	0.482477	+	0.835674i
$950$		0			0
$951$		−	1969.20i		−	2.07066i
$952$		0			0
$953$		−	188.561i		−	0.197860i	−0.995094	−	0.0989302i	$-0.968458\pi$
$953$		−	188.561i		−	0.197860i	0.995094	−	0.0989302i	$-0.0315421\pi$
$954$		0			0
$955$	374.272	−	980.013i	0.391908	−	1.02619i
$956$		0			0
$957$	886.499	−	1535.46i	0.926331	−	1.60445i
$958$		0			0
$959$	1194.81	+	896.745i	1.24590	+	0.935084i
$960$		0			0
$961$	−359.889	+	623.347i	−0.374495	+	0.648644i
$962$		0			0
$963$	−1527.17	+	881.710i	−1.58584	+	0.915586i
$964$		0			0
$965$	−974.880	+	792.204i	−1.01024	+	0.820937i
$966$		0			0
$967$			1088.32i			1.12546i	0.826640	+	0.562732i	$0.190250\pi$
$967$			1088.32i			1.12546i	−0.826640	+	0.562732i	$0.809750\pi$
$968$		0			0
$969$	1074.11	−	620.140i	1.10848	−	0.639980i
$970$		0			0
$971$	164.230	+	94.8183i	0.169135	+	0.0976501i	0.582178	−	0.813061i	$-0.302201\pi$
$971$	164.230	+	94.8183i	0.169135	+	0.0976501i	−0.413043	+	0.910712i	$0.635534\pi$
$972$		0			0
$973$	341.788	−	145.860i	0.351272	−	0.149907i
$974$		0			0
$975$	−1420.84	−	1270.56i	−1.45727	−	1.30314i
$976$		0			0
$977$	−687.092	+	396.693i	−0.703267	+	0.406032i	−0.808563	−	0.588409i	$-0.799754\pi$
$977$	−687.092	+	396.693i	−0.703267	+	0.406032i	0.105296	+	0.994441i	$0.466421\pi$
$978$		0			0
$979$		−	575.924i		−	0.588278i
$980$		0			0
$981$	−993.741			−1.01299
$982$		0			0
$983$	26.9121	+	46.6132i	0.0273775	+	0.0474193i	0.879390	−	0.476103i	$-0.157951\pi$
$983$	26.9121	+	46.6132i	0.0273775	+	0.0474193i	−0.852012	+	0.523522i	$0.824618\pi$
$984$		0			0
$985$	101.824	+	635.860i	0.103375	+	0.645543i
$986$		0			0
$987$	4.27767	+	10.0237i	0.00433401	+	0.0101557i
$988$		0			0
$989$	192.475	−	333.377i	0.194616	−	0.337085i
$990$		0			0
$991$	−718.340	−	1244.20i	−0.724864	−	1.25550i	−0.959030	−	0.283304i	$-0.908569\pi$
$991$	−718.340	−	1244.20i	−0.724864	−	1.25550i	0.234166	−	0.972197i	$-0.424764\pi$
$992$		0			0
$993$	−1725.80			−1.73797
$994$		0			0
$995$	−776.870	+	631.298i	−0.780774	+	0.634470i
$996$		0			0
$997$	110.002	+	190.529i	0.110333	+	0.191102i	0.915905	−	0.401396i	$-0.131475\pi$
$997$	110.002	+	190.529i	0.110333	+	0.191102i	−0.805572	+	0.592499i	$0.798142\pi$
$998$		0			0
$999$	612.417	+	353.579i	0.613030	+	0.353933i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.3.br.b.369.8		16
4.3	odd	2		70.3.h.a.19.1	✓	16
5.4	even	2	inner	560.3.br.b.369.1		16
7.3	odd	6	inner	560.3.br.b.129.1		16
12.11	even	2		630.3.bc.a.19.8		16
20.3	even	4		350.3.k.e.201.4		16
20.7	even	4		350.3.k.e.201.5		16
20.19	odd	2		70.3.h.a.19.8	yes	16
28.3	even	6		70.3.h.a.59.8	yes	16
28.11	odd	6		490.3.h.b.129.5		16
28.19	even	6		490.3.d.a.489.9		16
28.23	odd	6		490.3.d.a.489.16		16
28.27	even	2		490.3.h.b.19.4		16
35.24	odd	6	inner	560.3.br.b.129.8		16
60.59	even	2		630.3.bc.a.19.3		16
84.59	odd	6		630.3.bc.a.199.3		16
140.3	odd	12		350.3.k.e.101.4		16
140.19	even	6		490.3.d.a.489.8		16
140.39	odd	6		490.3.h.b.129.4		16
140.59	even	6		70.3.h.a.59.1	yes	16
140.79	odd	6		490.3.d.a.489.1		16
140.87	odd	12		350.3.k.e.101.5		16
140.139	even	2		490.3.h.b.19.5		16
420.59	odd	6		630.3.bc.a.199.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.h.a.19.1	✓	16	4.3	odd	2
70.3.h.a.19.8	yes	16	20.19	odd	2
70.3.h.a.59.1	yes	16	140.59	even	6
70.3.h.a.59.8	yes	16	28.3	even	6
350.3.k.e.101.4		16	140.3	odd	12
350.3.k.e.101.5		16	140.87	odd	12
350.3.k.e.201.4		16	20.3	even	4
350.3.k.e.201.5		16	20.7	even	4
490.3.d.a.489.1		16	140.79	odd	6
490.3.d.a.489.8		16	140.19	even	6
490.3.d.a.489.9		16	28.19	even	6
490.3.d.a.489.16		16	28.23	odd	6
490.3.h.b.19.4		16	28.27	even	2
490.3.h.b.19.5		16	140.139	even	2
490.3.h.b.129.4		16	140.39	odd	6
490.3.h.b.129.5		16	28.11	odd	6
560.3.br.b.129.1		16	7.3	odd	6	inner
560.3.br.b.129.8		16	35.24	odd	6	inner
560.3.br.b.369.1		16	5.4	even	2	inner
560.3.br.b.369.8		16	1.1	even	1	trivial
630.3.bc.a.19.3		16	60.59	even	2
630.3.bc.a.19.8		16	12.11	even	2
630.3.bc.a.199.3		16	84.59	odd	6
630.3.bc.a.199.8		16	420.59	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	560.br (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.51048 + 4.34828i) q^{3} +(-4.93710 + 0.790609i) q^{5} +(-2.74755 - 6.43824i) q^{7} +(-8.10505 + 14.0384i) q^{9} +(4.76531 + 8.25377i) q^{11} -15.1849 q^{13} +(-15.8323 - 19.4831i) q^{15} +(-11.6790 - 20.2287i) q^{17} +(9.15855 + 5.28769i) q^{19} +(21.0976 - 28.1102i) q^{21} +(-18.2632 - 10.5443i) q^{23} +(23.7499 - 7.80663i) q^{25} -36.2016 q^{27} -37.0510 q^{29} +(-13.4505 + 7.76565i) q^{31} +(-23.9265 + 41.4419i) q^{33} +(18.6551 + 29.6140i) q^{35} +(-16.9168 - 9.76693i) q^{37} +(-38.1214 - 66.0282i) q^{39} -37.7426i q^{41} +18.2540i q^{43} +(28.9166 - 75.7167i) q^{45} +(-0.155040 + 0.268537i) q^{47} +(-33.9019 + 35.3788i) q^{49} +(58.6400 - 101.567i) q^{51} +(8.87784 - 5.12562i) q^{53} +(-30.0523 - 36.9821i) q^{55} +53.0986i q^{57} +(3.10758 - 1.79416i) q^{59} +(96.8741 + 55.9303i) q^{61} +(112.651 + 13.6111i) q^{63} +(74.9693 - 12.0053i) q^{65} +(-11.0746 + 6.39394i) q^{67} -105.885i q^{69} +32.7865 q^{71} +(-30.1530 - 52.2266i) q^{73} +(93.5691 + 83.6728i) q^{75} +(40.0468 - 53.3579i) q^{77} +(-45.6617 + 79.0884i) q^{79} +(-17.9382 - 31.0698i) q^{81} -103.825 q^{83} +(73.6535 + 90.6374i) q^{85} +(-93.0158 - 161.108i) q^{87} +(-52.3329 - 30.2144i) q^{89} +(41.7213 + 97.7639i) q^{91} +(-67.5345 - 38.9911i) q^{93} +(-49.3972 - 18.8650i) q^{95} -130.271 q^{97} -154.492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{5} - 12 q^{9} + 12 q^{11} + 28 q^{15} + 12 q^{19} - 8 q^{21} - 42 q^{25} - 136 q^{29} - 84 q^{31} + 190 q^{35} - 312 q^{39} + 384 q^{45} + 296 q^{49} + 76 q^{51} + 372 q^{59} + 348 q^{61} - 104 q^{65}+ \cdots - 176 q^{99}+O(q^{100}) \) 16 * q - 6 * q^5 - 12 * q^9 + 12 * q^11 + 28 * q^15 + 12 * q^19 - 8 * q^21 - 42 * q^25 - 136 * q^29 - 84 * q^31 + 190 * q^35 - 312 * q^39 + 384 * q^45 + 296 * q^49 + 76 * q^51 + 372 * q^59 + 348 * q^61 - 104 * q^65 + 384 * q^71 + 150 * q^75 - 148 * q^79 - 140 * q^81 + 580 * q^85 - 912 * q^89 + 616 * q^91 + 310 * q^95 - 176 * q^99

Introduction

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